Chemistry: What is the mass of the matter inside a container

Question

Suppose 27.5g of sodium is reacted with 100.0g of chlorine in a sealed container to yield 70.0g of the compound NaCl. In the process, all of the sodium is consumed, but some of the chlorine is left over. What is the mass of the matter inside the container?

Answer 1

By the law of conservation of mass, since the container is closed and sealed, the mass before the reaction MUST equal the mass after the reaction.  Matter can not be created nor destroyed.  So, the quick answer would be 127.5 g (100.0 g + 27.5 g).  Now, to prove this, you can write the balanced equation for the reaction, then find moles NaCl formed and moles chlorine remaining and then convert to mass.  This is as follows:

2Na + Cl2(g) = 2NaCl  balanced equation

moles Na present = 27.5 g Na x 1 mole Na/23 g = 1.196 moles Na

moles Cl2 present = 100.0 g Cl2 x 1 mole/71 g = 1.408 moles Cl2

Since it takes 2 moles Na for each 1 mole Cl2, it is clear that Na in present in limiting amounts

Moles NaCl produced = 1.196 moles Na x 2 moles NaCl/2 moles Na = 1.196 moles NaCl

Moles Cl2 left over =1.408 moles - 0.598 moles = 0.81 moles Cl2 remaining

Mass NaCl at end = 1.196 moles NaCl x 58.5 g/mole = 69.97 g

Mass Cl2 at end = 0.81 moles Cl2 x 71 g/mole = 57.51 g

Total mass at end = 69.97 g NaCl + 57.51 g Cl2 = 127.48 g = 127.5 g (as predicted from law of conservation)